{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import math, random\n",
    "all_data  = pd.read_csv(\"sensor_data_600.txt\", delimiter=\" \", header=None, names = (\"date\",\"time\",\"ir\",\"z\"))#lidarのセンサ値は「z」に\n",
    "data = all_data.sample(3000).sort_values(by=\"z\").reset_index()  #1000個だけサンプリングしてインデックスを振り直す\n",
    "data = pd.DataFrame(data[\"z\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "##負担率の初期化## \n",
    "\n",
    "K = 3 #クラスタ数\n",
    "n = int(math.ceil(len(data)/K)) #クラスタあたりのセンサ値の数\n",
    "for k in range(K):\n",
    "    data[k] = [1.0 if k == int(i/n) else 0.0 for i,d in data.iterrows()] #データをK個に分けて、一つのr_{i,k}を1に。他を0に。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_parameters(ds, k, mu_avg=600, zeta=1, alpha=1, beta=1, tau=1): \n",
    "    R = sum([d[k] for _, d in ds.iterrows()])\n",
    "    S = sum([d[k]*d[\"z\"] for _, d in ds.iterrows()])\n",
    "    T = sum([d[k]*(d[\"z\"]**2) for _, d in ds.iterrows()])\n",
    "    \n",
    "    hat = {}\n",
    "\n",
    "    hat[\"tau\"] = R + tau\n",
    "    hat[\"zeta\"] = R + zeta\n",
    "    hat[\"mu_avg\"] = (S + zeta*mu_avg)/hat[\"zeta\"]\n",
    "    hat[\"alpha\"] = R/2 + alpha\n",
    "    hat[\"beta\"] = (T + zeta*(mu_avg**2) - hat[\"zeta\"]*(hat[\"mu_avg\"]**2))/2 + beta\n",
    "    \n",
    "    hat[\"z_std\"] = math.sqrt(hat[\"beta\"]/hat[\"alpha\"])\n",
    "    \n",
    "    return pd.DataFrame(hat, index=[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm, dirichlet\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def draw(ps):\n",
    "    pi = dirichlet([ps[\"tau\"][k] for k in range(K)]).rvs()[0]\n",
    "    pdfs = [ norm(loc=ps[\"mu_avg\"][k], scale=ps[\"z_std\"][k]) for k in range(K) ]\n",
    "\n",
    "    xs = np.arange(600,650,0.5)\n",
    "\n",
    "    ##p(z)の描画##\n",
    "    ys = [ sum([pdfs[k].pdf(x)*pi[k] for k in range(K)])*len(data) for x in xs] #pdfを足してデータ数をかける\n",
    "    plt.plot(xs, ys, color=\"red\")\n",
    "\n",
    "    ##各ガウス分布の描画##\n",
    "    for k in range(K):\n",
    "        ys = [pdfs[k].pdf(x)*pi[k]*len(data) for x in xs]\n",
    "        plt.plot(xs, ys, color=\"blue\")\n",
    "\n",
    "    ##元のデータのヒストグラムの描画##\n",
    "    data[\"z\"].hist(bins = max(data[\"z\"]) - min(data[\"z\"]), align='left', alpha=0.4, color=\"gray\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import digamma \n",
    "\n",
    "def responsibility(z, K, ps):\n",
    "    tau_sum = sum([ps[\"tau\"][k] for k in range(K)])\n",
    "    r = {}\n",
    "    for k in range(K):\n",
    "        log_rho = (digamma(ps[\"alpha\"][k]) - math.log(ps[\"beta\"][k]))/2 \\\n",
    "                            - (1/ps[\"zeta\"][k] + ((ps[\"mu_avg\"][k] - z)**2)*ps[\"alpha\"][k]/ps[\"beta\"][k])/2 \\\n",
    "                            + digamma(ps[\"tau\"][k]) - digamma(tau_sum)\n",
    "                \n",
    "        r[k] = math.exp(log_rho)\n",
    "       \n",
    "    w = sum([ r[k] for k in range(K) ]) #正規化\n",
    "    for k in range(K): r[k] /= w\n",
    "    \n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_step(ds): ###variationalinference2onestep\n",
    "    ##パラメータの更新##\n",
    "    params = pd.concat([update_parameters(ds, k) for k in range(K)]) \n",
    "\n",
    "    ##負担率の更新##\n",
    "    rs = [responsibility(d[\"z\"], K, params) for _, d in ds.iterrows() ]\n",
    "    for k in range(K):\n",
    "        ds[k] = [rs[i][k] for i,_ in data.iterrows()]\n",
    "        \n",
    "    return ds, params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "           tau         zeta      mu_avg       alpha          beta     z_std\n",
       "0  1203.406842  1203.406842  621.251814  602.203421   7131.042052  3.441160\n",
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       "           tau         zeta      mu_avg       alpha          beta     z_std\n",
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      "text/plain": [
       "           tau         zeta      mu_avg       alpha          beta     z_std\n",
       "0  1203.407018  1203.407018  621.251814  602.203509   7131.044198  3.441160\n",
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   ],
   "source": [
    "params_history = {} ###variationalinference2iter\n",
    "for t in range(1, 10000):\n",
    "    data, params = one_step(data)\n",
    "    if t%10 ==0:              #10回ごとにパラメータを記録\n",
    "        params_history[t] = params\n",
    "        display(params)\n",
    "        \n",
    "        if len(params_history) < 2:\n",
    "            continue\n",
    "           \n",
    "        if all([ abs(params_history[t-10][\"tau\"][k] - params_history[t][\"tau\"][k]) < 10e-5 for k in range(K)]):\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(params) ###variationalinference2draw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(params_history[100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(params_history[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{10:            tau         zeta      mu_avg       alpha         beta     z_std\n",
       " 0   993.604301   993.604301  620.705580  497.302150  5340.619442  3.277069\n",
       " 1   915.874983   915.874983  627.495038  458.437492  7488.235206  4.041566\n",
       " 2  1093.520716  1093.520716  632.150127  547.260358  6746.088652  3.510985,\n",
       " 20:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   957.563619   957.563619  620.867027  479.281809   5374.332028  3.348627\n",
       " 1   876.661535   876.661535  627.459489  438.830768  10506.333783  4.893021\n",
       " 2  1168.774846  1168.774846  631.535429  584.887423   7869.782899  3.668134,\n",
       " 30:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   933.936570   933.936570  620.926433  467.468285   5162.210649  3.323088\n",
       " 1   817.205510   817.205510  627.148849  409.102755  11267.621424  5.248074\n",
       " 2  1251.857921  1251.857921  631.298959  626.428960   8640.163555  3.713856,\n",
       " 40:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   919.694025   919.694025  620.963164  460.347012   4982.497568  3.289886\n",
       " 1   752.673377   752.673377  626.724630  376.836688  11029.993265  5.410172\n",
       " 2  1330.632598  1330.632598  631.201239  665.816299   9329.986401  3.743375,\n",
       " 50:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   913.877212   913.877212  620.997787  457.438606   4870.979705  3.263185\n",
       " 1   689.866011   689.866011  626.311166  345.433005  10448.546260  5.499789\n",
       " 2  1399.256778  1399.256778  631.138975  700.128389   9941.965026  3.768316,\n",
       " 60:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   915.722335   915.722335  621.027953  458.361168   4826.469529  3.244971\n",
       " 1   630.091955   630.091955  625.958335  315.545978   9725.493269  5.551681\n",
       " 2  1457.185709  1457.185709  631.087387  729.092855  10476.511257  3.790678,\n",
       " 70:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   923.523510   923.523510  621.053523  462.261755   4836.267089  3.234530\n",
       " 1   573.625584   573.625584  625.670865  287.312792   8967.294745  5.586673\n",
       " 2  1505.850906  1505.850906  631.040996  753.425453  10939.083558  3.810398,\n",
       " 80:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   935.393354   935.393354  621.075938  468.196677   4884.110622  3.229822\n",
       " 1   520.450454   520.450454  625.435737  260.725227   8229.624797  5.618217\n",
       " 2  1547.156192  1547.156192  630.998594  774.078096  11339.877482  3.827470,\n",
       " 90:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   949.827993   949.827993  621.096106  475.413997   4956.698104  3.228942\n",
       " 1   470.394411   470.394411  625.237931  235.697205   7532.417238  5.653143\n",
       " 2  1582.777596  1582.777596  630.959843  791.888798  11690.276309  3.842203,\n",
       " 100:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   965.775635   965.775635  621.114344  483.387817   5044.881829  3.230559\n",
       " 1   423.230872   423.230872  625.065062  212.115436   6878.204805  5.694445\n",
       " 2  1613.993493  1613.993493  630.924519  807.496747  12000.191926  3.854994,\n",
       " 110:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   982.534404   982.534404  621.130727  491.767202   5142.746829  3.233835\n",
       " 1   378.736772   378.736772  624.907524  189.868386   6263.210698  5.743441\n",
       " 2  1641.728825  1641.728825  630.892397  821.364412  12277.335022  3.866198,\n",
       " 120:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0   999.644176   999.644176  621.145278  500.322088   5246.562259  3.238266\n",
       " 1   336.714974   336.714974  624.757680  168.857487   5682.135612  5.800903\n",
       " 2  1666.640850  1666.640850  630.863257  833.820425  12527.414932  3.876095,\n",
       " 130:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1016.807087  1016.807087  621.158028  508.903543   5354.037341  3.243568\n",
       " 1   297.000025   297.000025  624.609072  149.000013   5129.893213  5.867607\n",
       " 2  1689.192888  1689.192888  630.836900  845.096444  12754.560893  3.884898,\n",
       " 140:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1033.833904  1033.833904  621.169022  517.416952   5463.850948  3.249594\n",
       " 1   259.458084   259.458084  624.455756  130.229042   4602.125557  5.944637\n",
       " 2  1709.708013  1709.708013  630.813158  855.354006  12961.704121  3.892764,\n",
       " 150:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1050.608323  1050.608323  621.178314  525.804161   5575.367523  3.256302\n",
       " 1   223.985643   223.985643  624.291686  112.492822   4095.266884  6.033630\n",
       " 2  1728.406034  1728.406034  630.791895  864.703017  13150.863780  3.899812,\n",
       " 160:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1067.062934  1067.062934  621.185958  534.031467   5688.476261  3.263732\n",
       " 1   190.508887   190.508887  624.109979   95.754444   3606.453071  6.137064\n",
       " 2  1745.428179  1745.428179  630.773013  873.214089  13323.342188  3.906126,\n",
       " 170:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1083.162808  1083.162808  621.192002  542.081404   5803.518004  3.272001\n",
       " 1   158.984561   158.984561  623.901858   79.992280   3133.389677  6.258686\n",
       " 2  1760.852631  1760.852631  630.756456  880.926316  13479.845395  3.911764,\n",
       " 180:            tau         zeta      mu_avg      alpha          beta     z_std\n",
       " 0  1098.894259  1098.894259  621.196488  549.94713   5921.290500  3.281313\n",
       " 1   129.403160   129.403160  623.654826   65.20158   2674.219575  6.404268\n",
       " 2  1774.702580  1774.702580  630.742217  887.85129  13620.539103  3.916761,\n",
       " 190:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1114.257264  1114.257264  621.199456  557.628632   6043.145873  3.291994\n",
       " 1   101.795795   101.795795  623.349089   51.397897   2227.400273  6.583039\n",
       " 2  1786.946941  1786.946941  630.730354  893.973471  13745.039043  3.921125,\n",
       " 200:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1129.260572  1129.260572  621.200952  565.130286   6171.237081  3.304546\n",
       " 1    76.247745    76.247745  622.949453   38.623872   1791.581277  6.810678\n",
       " 2  1797.491683  1797.491683  630.721008  899.245842  13852.313977  3.924840,\n",
       " 210:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1143.918210  1143.918210  621.201047  572.459105   6309.055474  3.319785\n",
       " 1    52.926522    52.926522  622.383573   26.963261   1365.441949  7.116237\n",
       " 2  1806.155268  1806.155268  630.714442  903.577634  13940.438594  3.927855,\n",
       " 220:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1158.242284  1158.242284  621.199897  579.621142   6462.628631  3.339124\n",
       " 1    32.149098    32.149098  621.466658   16.574549    947.339982  7.560179\n",
       " 2  1812.608619  1812.608619  630.711125  906.804309  14006.010377  3.930071,\n",
       " 230:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1172.192084  1172.192084  621.197982  586.596042   6643.145820  3.365250\n",
       " 1    14.597279    14.597279  619.496878    7.798639    533.831948  8.273568\n",
       " 2  1816.210637  1816.210637  630.711907  908.605319  14042.535689  3.931290,\n",
       " 240:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1185.068412  1185.068412  621.198119  593.034206   6862.827704  3.401823\n",
       " 1     2.535529     2.535529  609.764710    1.767764    104.224126  7.678422\n",
       " 2  1815.396060  1815.396060  630.718377  908.198030  14032.940201  3.930828,\n",
       " 250:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1192.298763  1192.298763  621.214956  596.649382   6997.890222  3.424711\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1809.701237  1809.701237  630.732937  905.350618  13949.005427  3.925213,\n",
       " 260:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1196.383195  1196.383195  621.228535  598.691597   7046.781732  3.430788\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1805.616805  1805.616805  630.745470  903.308403  13869.485081  3.918430,\n",
       " 270:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1198.966688  1198.966688  621.237084  599.983344   7077.629823  3.434585\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1803.033312  1803.033312  630.753421  902.016656  13819.089241  3.914105,\n",
       " 280:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1200.599969  1200.599969  621.242497  600.799985   7097.218050  3.436997\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1801.400031  1801.400031  630.758442  901.200015  13787.345159  3.911377,\n",
       " 290:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1201.632505  1201.632505  621.245922  601.316252   7109.636890  3.438525\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1800.367495  1800.367495  630.761614  900.683748  13767.324592  3.909657,\n",
       " 300:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1202.285252  1202.285252  621.248089  601.642626   7117.502008  3.439494\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1799.714748  1799.714748  630.763618  900.357374  13754.687022  3.908570,\n",
       " 310:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1202.697905  1202.697905  621.249459  601.848953   7122.479793  3.440106\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1799.302095  1799.302095  630.764884  900.151047  13746.705473  3.907884,\n",
       " 320:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1202.958775  1202.958775  621.250325  601.979387   7125.629003  3.440494\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1799.041225  1799.041225  630.765685  900.020613  13741.662698  3.907450,\n",
       " 330:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.123691  1203.123691  621.250873  602.061846   7127.620742  3.440739\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.876309  1798.876309  630.766191  899.938154  13738.475994  3.907176,\n",
       " 340:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.227948  1203.227948  621.251219  602.113974   7128.880245  3.440894\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.772052  1798.772052  630.766510  899.886026  13736.461927  3.907003,\n",
       " 350:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.293857  1203.293857  621.251438  602.146928   7129.676596  3.440992\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.706143  1798.706143  630.766713  899.853072  13735.188847  3.906893,\n",
       " 360:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.335522  1203.335522  621.251577  602.167761   7130.180101  3.441054\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.664478  1798.664478  630.766840  899.832239  13734.384147  3.906824,\n",
       " 370:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.361862  1203.361862  621.251664  602.180931   7130.498412  3.441093\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.638138  1798.638138  630.766921  899.819069  13733.875447  3.906780,\n",
       " 380:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.378515  1203.378515  621.251719  602.189257   7130.699699  3.441118\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.621485  1798.621485  630.766972  899.810743  13733.553857  3.906752,\n",
       " 390:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.389042  1203.389042  621.251754  602.194521   7130.826906  3.441134\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.610958  1798.610958  630.767005  899.805479  13733.350568  3.906735,\n",
       " 400:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.395697  1203.395697  621.251777  602.197849   7130.907352  3.441144\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.604303  1798.604303  630.767025  899.802151  13733.222054  3.906724,\n",
       " 410:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.399904  1203.399904  621.251791  602.199952   7130.958194  3.441150\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.600096  1798.600096  630.767038  899.800048  13733.140807  3.906717,\n",
       " 420:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.402564  1203.402564  621.251799  602.201282   7130.990315  3.441154\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.597436  1798.597436  630.767046  899.798718  13733.089453  3.906712,\n",
       " 430:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.404245  1203.404245  621.251805  602.202123   7131.010654  3.441156\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.595755  1798.595755  630.767051  899.797877  13733.056949  3.906710,\n",
       " 440:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.405308  1203.405308  621.251809  602.202654   7131.023532  3.441158\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.594692  1798.594692  630.767054  899.797346  13733.036453  3.906708,\n",
       " 450:           tau        zeta      mu_avg      alpha          beta     z_std\n",
       " 0  1203.40598  1203.40598  621.251811  602.20299   7131.031641  3.441159\n",
       " 1     1.00000     1.00000  600.000000    1.00000      1.000000  1.000000\n",
       " 2  1798.59402  1798.59402  630.767057  899.79701  13733.023480  3.906707,\n",
       " 460:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.406404  1203.406404  621.251812  602.203202   7131.036773  3.441160\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.593596  1798.593596  630.767058  899.796798  13733.015311  3.906706,\n",
       " 470:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.406673  1203.406673  621.251813  602.203336   7131.039989  3.441160\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.593327  1798.593327  630.767059  899.796664  13733.010088  3.906706,\n",
       " 480:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.406842  1203.406842  621.251814  602.203421   7131.042052  3.441160\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.593158  1798.593158  630.767059  899.796579  13733.006843  3.906705,\n",
       " 490:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.406949  1203.406949  621.251814  602.203475   7131.043343  3.441160\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.593051  1798.593051  630.767059  899.796525  13733.004750  3.906705,\n",
       " 500:            tau         zeta      mu_avg       alpha          beta     z_std\n",
       " 0  1203.407018  1203.407018  621.251814  602.203509   7131.044198  3.441160\n",
       " 1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       " 2  1798.592982  1798.592982  630.767060  899.796491  13733.003435  3.906705}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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